Same problem. Found a solution for now!
Hi fellow iPad sufferers,
Have been going mad for the past couple of weeks since my work gave me (and about 40 other staff) an iPad2 - such a pretty thing - and told us to learn how to use it! I think I'm the only one of the 40 with this major problem.
As with most contributors to this thread, I could connect to the internet via WiFi but browsing the net has been a very spasmodic occurrence - fine last night but nothing today and nothing most of last week. Everything is fine on the 6 other devices in the house (3 X Mac and 3 X PC), so I deduced that it's not a router problem. Nevertheless, I have tried every suggestion on this forum (power off, reboot router, forget network, reset network, brightness setting, update iTunes, etc) to no avail.
I can browse at work and at other people's homes but not consistently in my home.
I have fixed the problem twice now after reading suggestions online (I'm not particularly tech savvy. Well not all!). The first time, I changed to a static IP - I copied the numbers from my iPhone settings. But it has happened again.
Today I compared the numbers on the iPhone and iPad and noticed the DNS setting was different, so I copied the iPhone DNS setting onto the iPad and, hey presto (!), I'm able to browse and get on iTunes again etc. So now I think it's the DNS setting, not the static vs dynamic IP address.
Fingers-crossed this will be a permanent solution (I don't actually know what a DNS setting is, but it worked tonight!) As others have said, the iPad clearly has a problem retaining the settings, so I'm not optimistic but thought this might help someone.
Good luck.